The fact that our fairness guarantees are not data dependent, unlike [1]}, shows a major difference between approaches. It is not the most important one. With respect to ensuring fairness while remaining as close as possible to the empirical data, the max-ent approach of [1]} comes with downsides: optimal guarantees are on marginals, in small numbers for tractability (typically over single attributes) and one needs to hardcode the ones chosen to ensure the solution complies with fairness guarantees. This makes three key limitations, only one of which we do share. We are guaranteed to get a fairness compliant solution, provably converging to the best approximation with respect to the KL divergence, but there is also a complexity lever in our case – though arguably simpler to manoeuvre than for [1]}. Simply put, convergence is guaranteed as long as the weak learning assumption holds (Definition REF ). This implies that we should not choose models that are too simple to build the sequence of sufficient statistics \( c_{.}(\cdot ) \)  in the exponential family, Eq. (REF ) , which approximates \( P \) .
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